Question

Factor completely.9 - 25.22Show CalculatorStuck? Watch a video or use hint

Answer 1

Given the expression:

$9-25x^2$

9 is the exact square of 3

25 is the exact square of 5

So you can rewrite this expression as:

$(3^2)-(5x)^2$

Now considering the formula for the difference of squares:

$a^2-b^2=(a+b)(a-b)$

If we consider a=3 and b=5x, we can say that

$(3+5x)(3-5x)$

So we have that the steps to factor the given expression are:

$9-25x^2=(3)^2-(5x)^2=(3+5x)(3-5x)$

*-*-*-*-*-

$3x^2+0x-174$

In this case, none of the terms is a perfect square, so you have to use another method.

I'll ignore the 0x term, since its irrelevant, the expression is then:

$3x^2-147$

Both 3 and 147 are divisible by 3, so the first step will be to divide the expression by three to simplify it:

$\begin{gathered} \frac{3x^2}{3}-\frac{147}{3} \\ x^2-49 \end{gathered}$

Now the terms of the equation are expressed as exact squares.

x²= x*x

and

49=7²=7*7

We reached the lowest simplification, now we can determine the diference of squares using a=x and b=7

$\begin{gathered} (a+b)(a-b) \\ (x+7)(x-7) \end{gathered}$

Finally multiply the factoring by 3 → at the begining we divided it by 3 to simplify the expression but if you dont multiply the final factoring by 3 again the result won't be equivalent to the original equation.

So the factoring of 3x²+0x-147 is 3(x+7)(x-7)